Question: Simplify the following expression: $\dfrac{72a^2}{32a^3}$ You can assume $a \neq 0$.
$ \dfrac{72a^2}{32a^3} = \dfrac{72}{32} \cdot \dfrac{a^2}{a^3} $ To simplify $\frac{72}{32}$ , find the greatest common factor (GCD) of $72$ and $32$ $72 = 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3$ $32 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2$ $ \mbox{GCD}(72, 32) = 2 \cdot 2 \cdot 2 = 8 $ $ \dfrac{72}{32} \cdot \dfrac{a^2}{a^3} = \dfrac{8 \cdot 9}{8 \cdot 4} \cdot \dfrac{a^2}{a^3} $ $\phantom{ \dfrac{72}{32} \cdot \dfrac{2}{3}} = \dfrac{9}{4} \cdot \dfrac{a^2}{a^3} $ $ \dfrac{a^2}{a^3} = \dfrac{a \cdot a}{a \cdot a \cdot a} = \dfrac{1}{a} $ $ \dfrac{9}{4} \cdot \dfrac{1}{a} = \dfrac{9}{4a} $